Simplify the following expression: $k = \dfrac{a^2 - 7a - 8}{a - 8} $
Solution: First factor the polynomial in the numerator. $ a^2 - 7a - 8 = (a - 8)(a + 1) $ So we can rewrite the expression as: $k = \dfrac{(a - 8)(a + 1)}{a - 8} $ We can divide the numerator and denominator by $(a - 8)$ on condition that $a \neq 8$ Therefore $k = a + 1; a \neq 8$